Subgroups — C₂×#634⋊C₃ #88701

Order 432.

149 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₃⋊Dic₃)⋊C₃	C₂	1	2	yes	maximal
3	#634⋊C₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×#634	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×Dic₆	—	3	1	no	maximal
6	C₂²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
8	(C₃⋊Dic₃)⋊C₃	C₂²	1	4	yes	—
9	C₂×C₃²×C₄	—	2	1	no	—
10	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
11	C₂×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃⋊Dic₃	C₂×C₃	1	2	yes	—
13	#634	C₂×C₃	1	4	yes	complemented
14	C₂×C₃×Dic₃	—	3	2	no	—
15	C₃×Dic₆	—	3	4	no	—
16	C₂×H(3,𝔽₃)	Q₈	1	2	yes	complemented
17	C₂×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
18	C₂×C₃×Q₈	—	9	1	no	—
19	C₂×Dic₆	—	3	1	no	—
20	C₂×Dic₆	—	9	1	no	—
21	C₂²×C₃²	—	2	1	no	—
22	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
23	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
24	C₃²×C₄	—	2	2	no	—
25	C₃²×C₄	C₂×D₃	1	2	yes	—
26	C₃²×C₄	C₂²×C₃	1	2	yes	—
27	C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
28	C₃×Dic₃	—	3	4	no	—
29	H(3,𝔽₃)	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
30	C₃×Q₈	—	9	4	no	—
31	C₂×C₃×C₄	—	3	1	no	—
32	C₂×C₃×C₄	—	3	1	no	—
33	C₂×C₃×C₄	—	6	1	no	—
34	C₂×C₃×C₄	—	9	2	no	—
35	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
36	C₂×Dic₃	—	3	2	no	—
37	C₂×Dic₃	—	9	2	no	—
38	Dic₆	—	3	4	no	—
39	Dic₆	—	9	4	no	—
40	C₂×C₃²	—	2	2	no	—
41	C₂×C₃²	—	2	1	no	—
42	C₂×C₃²	Dic₆	1	2	yes	complemented
43	C₂×C₃²	C₃×Q₈	1	2	yes	complemented
44	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
45	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
46	C₂×Q₈	—	9	1	no	Sylow
47	C₂²×C₃	—	3	1	no	—
48	C₂²×C₃	—	3	1	no	—
49	C₂²×C₃	—	6	1	no	—
50	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
51	C₃×C₄	—	3	2	no	—
52	C₃×C₄	—	3	2	no	—
53	C₃×C₄	—	6	2	no	—
54	C₃×C₄	—	9	4	no	—
55	C₃×C₄	C₂×C₃×D₃	1	2	yes	—
56	Dic₃	—	3	4	no	—
57	Dic₃	—	9	4	no	—
58	C₃²	—	2	1	no	—
59	C₃²	C₂×Dic₆	1	1	yes	characteristic, complemented
60	C₃²	C₂×C₃×Q₈	1	1	yes	characteristic, complemented
61	Q₈	—	9	4	no	—
62	C₂×C₄	—	9	2	no	—
63	C₂×C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
64	C₂×C₃	—	3	2	no	—
65	C₂×C₃	—	3	2	no	—
66	C₂×C₃	—	3	1	no	—
67	C₂×C₃	—	3	1	no	—
68	C₂×C₃	—	6	2	no	—
69	C₂×C₃	—	6	1	no	—
70	C₂×C₃	C₃×Dic₆	1	2	yes	—
71	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
72	C₂²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
73	C₄	—	9	4	no	—
74	C₄	C₂×(C₃⋊D₃)⋊C₃	1	2	yes	—
75	C₃	—	3	1	no	—
76	C₃	—	3	1	no	—
77	C₃	—	6	1	no	—
78	C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
79	C₂	#634⋊C₃	1	2	yes	direct product factor
80	C₂	C₂²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×(C₃⋊D₃)⋊C₃
commutator, cosocle	C₂×C₃²	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×D₃
Fitting	C₂×C₄×H(3,𝔽₃)	C₂
socle	C₂²×C₃	C₂×C₃×D₃
prime radical	C₂²×H(3,𝔽₃)	C₂²
hypercenter	C₂×C₄	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₂×C₃×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #634⋊C₃	C₂	direct (N × H)
4. C₂×#634	C₃	semidirect
13. #634	C₂×C₃	semidirect
16. C₂×H(3,𝔽₃)	Q₈	semidirect
29. H(3,𝔽₃)	C₂×Q₈	semidirect
42. C₂×C₃²	Dic₆	semidirect
43. C₂×C₃²	C₃×Q₈	semidirect
59. C₃²	C₂×Dic₆	semidirect
60. C₃²	C₂×C₃×Q₈	semidirect
79. C₂	#634⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×H(3,𝔽₃)	2
C₂×(C₃⋊Dic₃)⋊C₃	2
#634⋊C₃	2
C₂×#634	3
C₂×C₃×Dic₆	3

Subgroups — C2×#634⋊C3 #88701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#634⋊C₃ #88701